Models of the Neuron (580.439/639)

Fall 2009

Course overview

This course treats single neuron modeling, including molecular models of channels and channel gating, Hodgkin-Huxley style models of membrane currents, non-linear dynamics as a way of understanding membrane excitability, neural integration through cable theory, and network computation. The goal of the course is to understand how neurons work as biological computing elements and also to give students experience with modeling techniques as applied to complex biological systems.

The course meets Mondays, Wednesdays, and Fridays from 9:00-10:00 a.m. and Tuesdays from 9:00-10:00 a.m. at Homewood in Hodson 305. The MWF classes are lectures and the T classes are recitations where homework will be discussed and help with Matlab provided; T classes are required for undergraduates and optional for graduate students. The course is taught by Eric Young, 505 Traylor at the Medical School, telephone 410-955-3164 (eyoung@jhu.edu); the T.A. is Aaron Wong, telephone 410-955-2904 (aaron.wong@jhu.edu). TA Office hours will be on Tuesday and Wednesday from 10-11 in Clark 311 or by appointment. The prerequisites are mathematics through linear algebra and differential equations and an introduction to neuroscience (e.g. 580.422, 080.205, or 080.304); introductory signal and system theory (e.g. 580.222 or 520.213-214) is helpful.

There is no required text, although Biophysics of Computation by C. Koch is an excellent book that covers most of the material in the course. Foundations of Cellular Neurophysiology by D. Johnston and S. Wu covers some of the material in a more elementary fashion and P. Dayan and L.F. Abbott Theoretical Neuroscience provides a more modern view of some topics. Several chapters from Methods in Neuronal Modeling (2nd ed.) edited by C. Koch and I. Segev will be used. An excellent and comprehensive book on membrane physiology is Ionic Channels of Excitable Membranes, (3rd ed.) by B. Hille. This book covers ion channels in more depth than those above; it is required reading for anyone seriously interested in this subject. Additional references include the following: G.M. Shepherd, The Synaptic Organization of the Brain (4th ed.) is a good introduction to neural systems for persons with no previous experience. S.H. Strogatz Nonlinear Dynamics and Chaos cover aspects of nonlinear dynamics and network theory that will be discussed in the course; some material from H.R. Wilson, Spikes Decisions and Actions will also be used. The book Dynamical Systems in Neuroscience by E.M. Izhikevich provides a useful view of 2nd-order nonlinear systems of the type used in neuroscience. A good overview of network theory is J. Hertz, A Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation. Finally, J.J.B. Jack, D. Noble, and R.W. Tsien, Electric Current Flow in Excitable Cells contains detailed discussions of older work, especially useful for cable theory. All of these are on reserve in Eisenhower library.

Weekly homework assignments will be given. Solutions should be handed in and will be graded. Two computer modeling projects will be assigned during the term. The grade for graduate students will be based on the midterm (20%), final (30%), the modeling projects (40%), and the homework (10%). Undergraduates will have the option of doing the second modeling project for extra credit, and their grade will be based on the midterm (30%), first modeling project (30%), final (30%), and homework (10%). Students are encouraged to discuss homework problems with colleagues, but the final product that is handed in should be the student's own work. Modeling projects must be done individually. A conscientious homework record will contribute to raising marginal grades.


Course schedule Updated August 18, 2009


Lectures are MWF 9-10 in Hodson 305. Parentheses indicates no class meeting on that day.

Sep. 2, 4  Introduction; review of neurophysiology and thermodynamics; equilibria, electrodiffusion.

        (7), 9, 11  I-V relationships; cellular steady state.

        14, 16, 18  Biological membranes and channels, the Kcsa and similar channels. Barrier models of channel permeation.

        21, 23, 25  Selectivity, independence. Voltage clamp analysis; gating.

        28, 30, Oct. 2  Hodgkin-Huxley and other models. Simulation methods for neural models.

Oct. 5, 7, 9 Phase-plane analysis of nonlinear systems, model reduction,  equilibrium points, linearization, classification of behavior near equilibrium points.

        12, 14, 16  Limit cycles, bursting, varieties of channels

        19, 21, 23  Role of calcium; neuromodulation. Examples of channel systems.

        26, 28, 30  MIDTERM EXAM OCT 26, 2009; Examples, cont’d: corticothalamic neurons; regulation of ion channel density.

Nov. 2, 4, 6  Cable equation, finite cylinders, the equivalent cylinder.

FIRST MODELING PROJECT DUE NOV. 9, 5:00 P.M.

        9, 11, 13  Rall motorneuron model; dendritic tree inverse problems; compartmental models.

16, 18, 20  Real dendritic trees, synaptic coupling to the soma, arrangement of synapses.

        23, 25, (27)  Spines and calcium; plasticity.  (Thanksgiving is the 26th.)

        30, Dec. 2, 4, 7  Neural networks; Stability of network fixed points; network dynamics. Liapunov functions and the Cohen-Grossberg theorem.

Dec. 15  FINAL EXAM 9-12 AM.

SECOND MODELING PROJECT DUE DEC 18, 5:00 P.M.

 


Homeworks

Homework assignments will be given weekly, and are generally due on Mondays by the end of class. They can be submitted in class or dropped off to the TA (notify TA if doing so). Homework will not be accepted after solutions are posted. The links below will return pdf files of the homework sets and solutions. The pdf files can be viewed with the free Adobe Acrobat Reader. Solution sets will be available for downloading after the due-date of the homework.

Homework 1 (due Monday, September 14)

Solutions to Homework 1

Homework 2 (due Monday, September 28)

Solutions to Homework 2

Homework 3 (due Monday, October 5)

Solutions to Homework 3

Homework 4 (due Monday, October 12)

Solutions to Homework 4

Homework 5 (due Friday, October 23)

Solutions to Homework 5

Homework 6 (due Monday, November 16)

Solutions to Homework 6

Homework 7 (due Monday, November 23)

Solutions to Homework 7

 


Course notes

  1. Review of circuit theory and differential equations
  2. Thermodynamics and Transport
  3. Channels, Selectivity, and Permeation
  4. Nonlinear Dynamics and Hodgkin Huxley Equations
  5. Cable Theory
  6. Papers on Dendritic Processing

Class lectures


Other relevant notes


Modeling projects

Two computer modeling projects will be assigned. All work on the modeling projects must be done individually.

 

Project #1 : DUE MONDAY, NOVEMBER 9, 5:00 P.M.

For undergraduates in 580.439, parts 1-6 are due in class on Friday, October 30.

Please download the following to get started :
- Project #1 Instructions

- Supporting code

 

Project #2 : DUE FRIDAY (DECEMBER 18), 5:00 P.M.

(email pdf to eyoung@jhu.edu)

Please read the following to get started :
- Instructions/Description/Suggestions
Project Proposal Due on Monday, NOVEMBER 16

 


Previous exams



Copies of previous midterms and finals are posted below, along with solutions.

Midterm exam, 2009

Midterm exam solutions 2009

Midterm exam, 2008

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Midterm exam, 2007

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Midterm exam, 2006

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Midterm exam, 1999

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Midterm exam, 1998

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Midterm exam, 1997

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Final exam, 2008

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Final exam, 2007

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Final exam, 2006

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Final exam, 2004

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Final exam, 2002

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Final exam, 2001

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Final exam, 1999

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Final exam, 1998

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Final exam, 1997

Final exam solutions 1997